Brine transport in porous media: self-similar solutions |
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| Institution: | 1. P.O. Box 94079, 1090 GB Amsterdam, The Netherlands;2. Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands;3. Department of Watermanagement, Environmental and Sanitary Engineering, Delft University of Technology, P.O. Box 5048, 2600 GA Delft, The Netherlands;1. GFZ German Research Centre for Geosciences, Potsdam, Germany;2. RWTH Aachen University, Department of Geology, Geochemistry of Petroleum and Coal, Aachen, Germany;3. Centre for Earth Evolution and Dynamics (CEED), Department of Geosciences, University of Oslo, Oslo, Norway;4. Research Centre for Arctic Petroleum Exploration (ARCEx) University of Tromsø, Tromsø, Norway;1. Department of Electrical and Computer Engineering, Tufts University, 196 Boston Avenue, Medford, MA 02155, United States;2. Department of Civil and Environmental Engineering, Yang & Yamazaki Environment & Energy Building, 473 Via Ortega, Stanford, CA 94305, United States;3. Institute for Computational and Mathematical Engineering, Huang Engineering Center, 475 Via Ortega, Stanford, CA 94305, United States;1. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China;2. School of Civil and Resource Engineering, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia;1. Institute of Geological Sciences, Jagiellonian University, Oleandry 2a, 30-063 Kraków, Poland;2. Department of Geosciences, Williams College, Williamstown, MA 01267 USA;3. CIBIO-Açores, Centro de Investigação em Biodiversidade e Recursos Genéticos, InBIO Laboratório Associado, Pólo dos Açores, Açores, Portugal;4. Departamento de Biologia, Universidade dos Açores, 9501-801 Ponta Delgada, Açores, Portugal;5. MPB-Marine PalaeoBiogeography Working Group of the University of the Azores, Rua da Mãe de Deus, 9501-801, Portugal;6. SMNS - Staatliches Museum für Naturkunde Stuttgart, Rosenstein 1, 70191 Stuttgart, Germany;7. Departamento de Geociências, Universidade dos Açores, Ponta Delgada, Portugal;8. School of Earth Sciences, University of Bristol, Wills Memorial Building, Queen''s Road, Bristol, BS8 1RJ, UK;1. Institute of Earth Sciences, Hebrew University of Jerusalem, Givat-Ram Campus, 91904, Israel;2. Geological Survey of Israel, 32 Yeshayahu Leibowitz st., 9371234 Jerusalem, Israel |
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| Abstract: | In this paper we analyze a model for brine transport in porous media, which includes a mass balance for the fluid, a mass balance for salt, Darcy's law and an equation of state, which relates the fluid density to the salt mass fraction. This model incorporates the effect of local volume changes due to variations in the salt concentration. Density variations affect the compressibility of the fluid, which in turn cause additional fluid flow. Two specific situations are investigated that lead to self similarity. We study the relative importance of the compressibility effect in terms of the relative density difference. Semi-analytical solutions are obtained as well as asymptotic expressions in terms of the relative density difference. It is found that the volume changes have a small but noticeable effect on the mass transport only when the salt concentration gradients are large. Some results on the simultaneous transport of brine and dissolved (radioactive) tracers are presented. |
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